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Charmonium I: Introduction & Production Models. Thomas J. LeCompte Argonne National Laboratory. Preliminaries. Thanks to the organizers for inviting me! I had a great time in the Dairy State, and I learned a lot. I talk too fast – so slow me down by interrupting me with questions! - PowerPoint PPT Presentation
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1
Charmonium I:Introduction & Production
Models
Thomas J. LeCompteArgonne National Laboratory
2
Preliminaries
Thanks to the organizers for inviting me! I had a great time in the Dairy State, and I learned a lot.
I talk too fast – so slow me down by interrupting me with questions!
In this talk, I try to distinguish between what is: Calculated Measured Inferred Just my opinion
If you can’t tell, speak up!
3
An Introduction To Charmonium
3 GeV
3.8 GeV
J/
(2S) or ’
3S1
3S1
3P2
3P1
3P0
2
1
0
Charmonium is a bound stateof a charmed quark andantiquark. It is “almostnonrelativistic”: ~ 0.4:Hence the hydrogen atom-likespectrum
Only the most important(experimentally) statesare shown. Many morewith different quantum numbers exist.
States can make radiative (E1) transitions to the other column.
Mas
s
thresholdDD
4
Review: Quantum Numbers
JS L12
Total Angular Momentum
Orbital Angular Momentum
Spin Angular Momentum 1
3/ SJ Means: Quark Spin=1 (3 = 2 x 1 + 1) Quark Orbital Ang. Mom. = 0 Total J/ Spin = 1
1PCJMeans: Total J/ Spin = 1 Parity is Odd Charge Conjugation is Odd
5
An Introduction To Charmonium
3 GeV
3.8 GeV
J/
(2S) or ’
3S1
3S1
3P2
3P1
3P0
2
1
0
Charmonium is a bound stateof a charmed quark andantiquark. It is “almostnonrelativistic”: ~ 0.4:Hence the hydrogen atom-likespectrum
Only the most important(experimentally) statesare shown. Many morewith different quantum numbers exist.
States can make radiative (E1) transitions to the other column.
Mas
s
thresholdDD
Repea
t of t
he Las
t Slid
e
6
Quarkonium Potential
A not-too-terrible model of the quark-antiquark force law:
Brr
AF
2
A Coulomb-like part
A spring-like part
This piece comes from the non-Abelian nature of QCD: the fact that you have 3-gluon and 4-gluon couplings.
In QED, there is no coupling, sothis term is absentThis is just like QED:
(sometimes called the“chromoelectric”
force)
4 E
QCDQCDE 4
This will be discussed in more detail in tomorrow’s talk
There are MUCH better potential models than what I have shown. These models use the quarkonia spectra to fit their parameters.
7
Discovery of the J/
e+e- annihilation at SPEAR
p + Be→ e+e- + X at AGS
October, 1974 Near
simultaneous discovery
Ting et al. at BNL AGS
Richter et al. at SLAC SPEAR
Quarks were no longer mathematical objects, but particles that moved in a potential
This work got the 1976 Nobel prize in physics
c.f. Fred Olness’ talk
8
Aside: Why ?
Mark I (SPEAR) Event Display
Decay is: (2S) → J/ + + + -
Followed by J/ → e+e-
It’s very convenient tohave the particle nameitself!
9
Homework
#1 – For each quarkonium (i.e. charmonium and bottomonium) state in the PDG, give Quantum numbers: k, n, L, S (like the Hydrogen atom) Spin, parity and charge-conjugation parity
#2 – The J/ is not the charmonium ground state; it’s the first excited state. Why was charmonium discovered with this state as opposed to the ground state? (The same is true for bottomonium)
#3 [version for theorists] Assume that the “springy” part of the force can be treated as a perturbation to the Coulomb potential (reminder: think “Laguerre polynomials”), and calculate the mass differences of the (2S) and states and of the (2S) and J/ states; from this extract values for A and B in the force law (slide 5). Hint: you should get a term like 5n2 + 1 –3l(l+1) .
[version for experimenters] Ask one of your theorist colleagues what the answer to #3 is.
10
Why is the J/ so Narrow?
J/ → open charm is kinematically blocked m(J/) < 2m(D)
J/ → gg → hadrons is blocked by quantum mechanics J/-g-g coupling is zero: more on this
later
J/ → ggg → hadrons is allowed (but suppressed) But now there are three powers of s. This is ~2/3 of the partial width
J/ → * → hadrons/leptons is allowed This is ~30%of the partial width There is also a few percent of radiative
transitions
Together, thisis called the “OZI Rule”
Strong decays aresuppressed so muchthat EM decaysare competitive
keV588)/( J
11
So How Are J/’s Produced?
Theory #1 – Drell-Yan Production Idea: the electromagnetic decay partial width (~26 MeV) is
about half that of the strong decay partial width (~59 MeV). Production rates should be comparable, but the input channel of quark and antiquark is (possibly) more accessible, so maybe this dominates.
Prediction: the J/ cross-section should be 4x higher for - beam as + beam:
2)( qQ 4)3/1(
)3/2(
)(
)(
)/(
)/(2
2
2
2
dQ
uQ
XJN
XJN
Aside: this prediction assumes an equal number of u and d quarks in the target. This is (incorrectly) called an “isoscalar” target. Even with non-isoscalar targets, the effect is small: Fe has 5% more d quarks than u-quarks.
What do the data show? …
Apology: I am only going to discuss hadroproduction today. Photoproduction is an interesting story, and there is some very high-
quality data from HERA.
12
A Typical Fixed Target Experiment
Magnet
Muon Shield
DownstreamTracking
Beam
Target
HadronAbsorber
+
-
Muon Detector
This kind of experiment looks only at the muons produced, and thus can
tolerate very high rates. // JXNp
Examples: CERN NA3,FNAL E-537
13
J/ Production with + and + beams
Pion Beam Charge Comparison
0
2
4
6
8
10
12
14
16
18
10 15 20 25 30 35
sqrt(s) (GeV)
nb
/nu
cleo
n
negative pions
positive pions
E-537
E-672/706
NA3
NA3
NA3
E-331
E-444
E-705
14
Inferences from the Measurement
The cross-section might be 10% or 15% larger for - beam, but it is certainly not a factor of 4. This is true for all energies and all targets
Targets: H, Be, Li, C, Fe, Cu, W, and Pt
Drell-Yan cannot be the dominant production mechanism for J/’s
Theory #2 – QCD quark-antiquark annihilation Idea: maybe the production is still initiated by quark-
antiquark annihilation, but mediated by gluons rather than photons
Prediction: + and - production is nearly equal Quark content has different electrical charge, but the same
color charge Prediction: production from antiproton beams – which
contain valence antiquarks - should be substantially (factor of >5-10) larger than production from proton beams
This difference should be even bigger at low energy
15
Production with p and pbar beams
Proton/Antiproton Comparison
0
2
4
6
8
10
12
14
16
18
10 15 20 25 30 35
sqrt(s) (GeV)
nb
/nu
cleo
n
Pbars
Protons
E-537
NA-3
NA-3E-331
E-444
E-705
E-672/706UA-6
16
Inferences from the Measurement
Production from pbar beams is larger than from proton beams, and the difference is greatest at lowest energy Theoretical success?
Instead of being a factor 5-10 difference, it’s (at most) 50%, and more typically 20-25%
Quark-antiquark annihilation cannot be the dominant production mechanism for J/’s It can be a piece of it, but not a very large piece
Conclusion – whatever process produces J/’s, it must be gluon induced Process of elimination: if it’s not the quarks…
17
The Trouble With Gluons
Remember, we know that J/ → gg is forbidden J/ is a 3S1 (1--) state Violates charge conjugation parity
Left side is C odd, right is C even If that isn’t bad enough, spin-statistics forces the amplitude
to be zero
That means gg → J/ is also forbidden ggg → J/ requires a 3-body collision
Infinitesimal rate
There seems to be no mechanismthat allows gluons to fuse intoa 3S1 state like the J/
18
The Color Singlet Model (CSM)
A J/ (or any charmonium particle) is a bound state of a charmed quark and antiquark in a color singlet state.
Therefore, one calculates the production of such a state The TOTAL production rate is the sum of the direct production
rate plus the production rate as the daughter of some other particle
Note BF( → J/ + ) are 30% and 13%
Predictions: Virtually all J/s come from the decays of ’s. 0:1:2 = 15:0:4
This is because gg → is suppressed, but gg → is allowed Virtually all (2S)’s come from the decays of b’s
m((2S))>m(), so production from decay is kinematically blocked
19
A 2d Generation Fixed Target Experiment
Magnet
Muon Shield
DownstreamTracking
Beam
Target
UpstreamTracking
+
-
Muon Detector
This kind of experiment also looks at particlesproduced in association with the J/.
/?)(/ JXNp
Examples: FNAL E-705, 706/672 Calorimeter
20
Selected Results
Experiment Sqrt(s) (GeV)
Fraction of J/’s from ’s
E-610 20.5 37%
E-672/706 31 44%
E-673 18.9-21.6 31-47%
E-705 24 40%
E-771 39 44%
GAMS 8.4 44%
HERA-B 41.5 32%
R806 62 47%
WA11 18.6 30%
Strangely, this did not seem to kill the CSM…
Worse, many experiments saw (2S) production even when (b) was small or zero.
21
More Selected Results
Experiment Sqrt(s) (GeV)
Ratio
E-610 20.5 0.9 ± 0.4
E-672/706 31 0.57 ± 0.19
E-673 18.9-21.6 0.96 ± 0.64
E-705 24 0.52 +0.57 –0.27
E-771 39 .53 ± .22
WA11 18.6 1.5 ± 0.6
This STILL did not seem to kill the CSM…
A typical experiment (E-771)
CSM predicts only the rightpeak is there.
CSM Prediction is 0This ensemble of measurementsis 4.2 different from 0
22
A Typical Colliding Beam Experiment
Muon detectors
Calorimeter:detects photons & Serves as hadron absorbers for muon detection
Outer tracker: in 1.5-2 T
magnetic field
Silicon vertex detector– for precision track impact parameter measurementBeams-eye view of a typical detector
+
-
23
The Plots That Finally Killed the CSM
J/’s not from ’s or b’s (2S)’s not from b’s
Theory and Measurement Disagree by a factor ~50 (red arrows)Even astronomers would call this poor agreement!
24
Ingredients of the last plot
Start with the J/cross-section
Remove the events that comefrom bottom quark decays
25
Ingredients of the last plot II
From (2S) decay
From decay
2/3 of the J/’s are produced directly.
This is not the few %predicted by the CSM
There are more current and accurate results from D0 and CDFbut they don’t change this picture – just bring it into sharper focus
26
Why Did It Take So Long for the Color Singlet Model to Die?
Maybe it’s because fixed target experiments were at lower pT, so the predictions were thought to be less reliable But this complaint was not leveled against Drell-Yan and
direct photon experiments at fixed target energies
Maybe a single definitive experiment was more convincing than an ensemble of experiments
Maybe it was lack of theoretical alternatives Hold that thought…coming up is the color evaporation
model…
Maybe it was simply better plotsmanship by the collider experiments
Maybe this should be the subject of somebody’s sociology PhD thesis
27
The Color Octet Model
It’s fairly clear that the CSM is missing some source of J/’s By the rate, it appears to be the dominant source
Consider the addition of two SU(3) (color) octets 8+8 = 1 + 8 + 8 + 10 + 10bar + 27 This allows 8+8 = 8: i.e. two gluons can be in a color octet state This is analogous to the three-gluon vertex
Think of this as a two-step process 1. The charm-anticharm pair is produced in a color octet state 2. The octet state radiates a gluon, and becomes colorless
gSPgg 138
23
The J/
This gets us our third gluon painlessly.
Instead of ggg → J/, we have gg → J/ + g
This is analogous to production:instead of a singlet radiating a photonthere is an octet “” radiating a gluon.
Other octet states also contribute
28
No Free Lunch
The Color Octet Model gives us a third gluon “for free” Because it’s soft, there is little penalty for an extra power of s
For exactly the same reason, the matrix element for the coupling between the octet c-cbar and the J/ + gluon is non-perturbative
It must be fit from experiment
All is not lost There are only a small number of non-perturbative parameters While they have to be fit from experiment, they have to be
consistent across different measurements There is at least one other prediction (later in this talk)
Strictly speaking, the COM accommodates a largecross section – it doesn’t predict it.
29
Fitting COM Parameters
A consistent set of COM parameters can predict reproduceboth the measured J/ and (2S) cross-sections
A major success of the model!
30
Ranting and Raving about Polarization
You may have heard talk of J/ polarization. This is wrong. Polarization means <Jz> ≠ 0
Various symmetries force <Jz> = 0 in J/ production J/’s are unpolarized
Since the J/ is a vector particle, there are two states that have <Jz> = 0 There is the (0,1,0) state – “transverse” There is the (1,0,1) state – “longitudinal” A commonly used convention is = (T - 2L)/(T + 2L)
Angular distribution of muons from J/ decay follows 1 + cos2() = 0 is called – incorrectly – “unpolarized”
The correct terminology is “spin alignment” <Jz> = 0 does not mean that the density matrix is equally populated The literature is chock-full of people using the wrong terminology –
only you can help end this! Make sure your next paper doesn’t do this!
This is just as important as “Deep-Inelastic Scattering” – the dash, not the space – from George Sterman’s lecture.
31
COM Alignment Predictions
At low pT (near zero), is or close to zero
At high pT (pT >> m(): perhaps 20 or 30 GeV) is large Would be 1, but diluted by higher order effects and contamination
from indirect production (e.g. decay) Probably 0.5-0.8 is what’s expected
Experimentally, high || events have one “stiff” (high pT) muon and one “soft” (low pT) muon
Low || events have two muons of similar pT
The measurement revolves around measuring the relative yields of these two classes of events
Not easy: detector geometry and triggering considerations make it easier to get events with muons of nearly equal pT’s than events with very different pT’s
Understanding and quantifying this effect is the experimental challenge in this measurement
J
2cos1d
d
is the + direction withrespect to the J/ direction
of motion in the J/ rest frame.
(Which technically makes no sense, but you all understand what I mean)
32
Spin Alignment Data
This matches BaBar’s result (they have much smaller uncertainties) when boostingthe measurements into theappropriate frame.
It is difficult to characterizethis as good agreementbetween prediction and data.
33
Color Evaporation
Basic idea: charm-anticharm pairs are produced in a color octet state These quarks emit one or more gluons in the process of
forming a colorless charmonium meson No attempt to understand this microscopic behavior in
detail is made Many theorists find this unsatisfying
Predictions? Not many – most of the information gets washed out during
the color evaporation Many experimentalists find this unsatisfying
Relative yields of different charmonium states goes as ~(2J+1)
This actually agrees rather well with the data Small or zero spin-alignment parameter
The red-headed stepchild of quarkonium production theories
34
The Joy of X: X(3872)
At Lepton-Photon 2003, Belle announced a new charmonium state seen in B decays You don’t get a new charmonium state every day Much less an unpredicted one!
(2S)
m(J/ +-) - m(J/)
Belle304M B’s
Eve
nts/
10 M
eV
?
Blow-up of right-hand peak
35
More Joy of X
With a speed uncharacteristic of hadron colliders, both CDF and D0 confirmed this particle Also, they identified that it is produced both promptly and
in B decays
D0
36
Dipion Mass X-perimental Results
Belle shows the dipion mass distribution to be peaked at high m() for the (2S).
This was explained by Brown and Cahn (1975) as a consequence of chiral symmetry.
I find the paper somewhat difficult to follow: “by theorists, for theorists.”
Belle’s measurement of m() is peaked at large mass.
CDF confirms this qualitatively.
Obscure and under-noticed m() prediction by Yan.Note the D-wave is not so prominent at high mass.
BelleBelle
37
What is the cause of all the X-Citement?
Charmonium? It has to have the right quantum numbers to decay to and It has to have the wrong quantum numbers to decay to a pair of D-
mesons
Options are: hc: (1P1) – mass too low: should be near the center of mass of the ’s,
or 3525 GeV First radial excitation h’c: 1P1(2P) – okay, so where is the regular hc
then? 2: (3D2): potential models predict this around 3790 MeV
Why the peak in the wrong spot? Should also decay to 1 + : not observed
Prediction exists for the m() spectrum – agreement not great
h3c: (1F3): potential models predict this around 4000 MeV Again, why is the peak in the wrong spot? No quantitative prediction exists for the m() spectrum, but since the two
pions are in a relative l = 2 state, the centrifugal barrier will favor a large m().
38
X-otic possibilities
No charmonium states seem to match the data If it’s charmonium, there’s something we don’t understand also
going on This may be related to the state’s proximity to DD* threshold
Could this be a bound state of a D and an anti-D*? Naturally explains the mass – just under threshold We know hadrons bind – we’re made of bound hadrons!
Not only are there nuclei in QCD, there are “hypernuclei” The high m() may be from the decay +
But watch out – the kinematics are such that any high mass enhancement looks like a
There may be precedent with a kaon anti-kaon bound state in the f0(980) and it’s isotriplet partner the a0(980)
These are 0++ states that fit poorly into the meson nonet The f0 is narrow on the low mass side, where it decays to , but wide on
the high mass side, where it decays to KK Other, more advanced arguments: c.f. Jaffe and Weinstein
Whatever it is, it looks like it will take more data to figure out exactly what is going on.
A new kind ofstrongly interacting matter?
39
Summary
Many theories have been put forward to explain charmonium hadroproduction
All have their problems Drell-Yan: -/+ cross section ratio Quark-antiquark: pbar/p cross section ratio Color Singlet: inclusive J/ cross section Color Octet: spin alignment Color Evaporation: not very predictive
All it’s got going for it is agreement with experiment
Still an open issue Most people seem to feel that the best shot is some variation of the
Color Octet picture Either a more advanced version that predicts a smaller spin alignment Or maybe the experimental problem will go away with better
measurements
Charmonium still has the potential to surprise us For example, the mysterious X(3872)